Random matrices in statistics: testing in spiked models
Iain Johnstone, Stanford University
Viernes 7 de marzo, Departamento de Matemáticas, aula 520, 11:30
Abstract.
Principal components analysis is a staple of multivariate statistical analysis. Viewed as the study of the eigenvalues of a sample covariance matrix, it is an important example for random matrix theory. The talk will explore the interplay between these two subjects by focusing on covariance matrices which are drawn from low rank perturbations of a scaled identity matrix. Such models arise in settings as diverse as finance, genetics and signal processing -- brief examples will be given. We give an overview of some results of several people on estimating and testing in settings with both weak and strong signals.